Proof of Haag's asymptotic condition for a two-dimensional quantum field theory

The quantum field theory is considered in this paper on an axiomatic basis in a two-dimensional space-time. Calculating the vacuum expectation of the product of the field operators, the author shows that in the two-dimensional case the generalized Kallen-Willhelmsson functions of all orders are expressed by those of the third order. An explicit form of this function is found. A simple proof is given of Haag's asymptotic condition, which also holds for an unfixed time.